How to change curve type?
Okay, so there are two main kinds of curves in Blender. Bézier and NURBS. A path is a NURBS curve and you want to convert a bezier curve to it. To do this is really easy: 


Click on the bezier curve in question.
Press Tab 
Select the bezier curve by pressing A
Press Space and search for "Set Spline Type"
Click "NURBS"


Now you have a "path" or NURBS curve to work with. I found this solution in reverse on here.

As for the practical difference between the two, as far as i can tell, the NURBS curve is more accurate and precise than its bezier counterpart. I hope this helps.